Pollock or Not? Can Fractals Spot a Fake Masterpiece?

A new study attacks the technique of using fractals, the repeating patterns found in everything from coastlines to fern fronds, to help distinguish authentic Jackson Pollock drip paintings from paint splattered by lesser hands.

In a paper submitted for publication to a major physics journal, researchers report that previously published criteria for identifying genuine Pollocks based on the presence of fractals—patterns that recur in varying sizes like Russian dolls nested inside one another—would wrongly grant Pollock status to a pair of amateur drip paintings.

Some researchers, however, are skeptical that the new method faithfully replicates that of University of Oregon physicist Richard Taylor, who first reported eight years ago that five Pollock paintings contained distinctive splatters within splatters, which he has attributed to the way "Jack the Dripper" swayed over the canvas while dribbling paint from brushes, sticks or straight from the can.

The Pollock–Krasner Foundation, which represents the estates of Pollock and his wife Lee Krasner, commissioned Taylor last year to examine six of 32 alleged Pollock drip paintings for fractal clues as to whether the master dripper (dead since 1956) had truly created them; the paintings, discovered in 2003, turned up fractalless.

Upon learning the news, physicists Katherine Jones–Smith and Harsh Mathur of Case Western Reserve University in Cleveland, Ohio, published their own Nature paper reporting the discovery of a similar fractal signature in quick sketches of different size stars or circles.

Jones–Smith had drawn the images two years earlier while preparing a presentation on Taylor's work, which she initially believed was correct. Much to her surprise, she discovered that her unsophisticated images contained seemingly identical fractal patterns.

To rebut the obvious counterargument—that stars look nothing like drip paintings—she, Mathur and Case Western cosmologist Lawrence Krauss have now analyzed three known Pollock drip paintings that Taylor had not examined in detail: Free Form (1946), Untitled (circa 1950) and Wooden Horse: Number 10A, 1948.

After using one of two separate computer techniques to isolate splatter marks of different colors, the researchers scanned for fractals in each layer of color by digitally counting colored pixels (or boxes) of various sizes. In this type of fractal, the number of boxes of each size relates to the box size raised to a power that holds constant over a range of sizes.

None of the Pollocks met stringent fractal criteria, although Free Form did satisfy what they consider a loose definition of a fractal and Wooden House failed its test in only two of six colors, they report in their paper submitted to Physical Review Letters, which has yet to be reviewed by other scientists.

Further complicating matters, the researchers identified fractals in two drip paintings created for the study by students [see image above]. They next examined two of the alleged Pollocks studied by Taylor, one of which, chosen for its resemblance to Free Form, passed the loose fractal test, whereas the other, resembling Wooden Horse, failed the test.

The new results clash with a 2006 Pattern Recognition Letters paper in which Taylor and colleagues reported identifying an identical fractal pattern in 14 known Pollocks but not among 37 drip paintings by University of Oregon undergraduates or 14 paintings of unknown origin thought to date to Pollock's era.

"Our position," Mathur says, "is that fractal analysis doesn't allow you to have a position" on the authenticity of a Pollock.

Hany Farid, a professor of computer science at Dartmouth College in New Hampshire who has followed the debate, says he sees flaws in the new study. "I think they took a fairly simplistic way of separating those colors," which he says could have skewed their results.

Taylor argues that the researchers applied his fractal criteria incorrectly on Untitled and notes that their Wooden Horse analysis hinges on paint covering less than 5 percent of the canvas, which makes drawing conclusions tricky.

Moreover, he says, the group's conclusion turns on a misconception. "There's an image out there of fractal analysis where you send the image through a computer and if a red light comes on it means it isn't a Pollock and if a green light comes on it is. We have never supported or encouraged such a mindless view."

Even if the new results are correct, Farid says, fractal analysis can still serve as one piece of evidence in the broader puzzle of authentication, which also involves historical and aesthetic judgments. Earlier this year, for example, a Harvard team reported that two pigments found in the 32 alleged Pollocks were not used in paints before 1996 and 1971.

"None of these tools stands by itself," Farid says.

Owners of authentic Pollocks, however, do stand to make a lot of money. Last year, the Pollock painting No. 5, 1948, was reportedly sold to a Mexican financier for a record $140 million.

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